%% Temple university CIS 2033
% A modern Introduction to Probability and Statistics
% Chapter 4 - Discrete random variables
%
% Author: Djordje Gligorijevic
% email: gligorijevic@temple.edu

%% Example 1
% Plot the PMF of a binomial distribution by varying p
%
% N = 100;
% p = {0.1, 0.5, 0.9}

N = 100;
X = 1:100;
P = [0.1, 0.5, 0.9];
Y = zeros(100,3);
% linestyle = cellstr(['-r'; '-b'; '-k'; '-g';'-m']);
linestyle2 = cellstr(['.r'; '.b'; '.k'; '.g';'.m']);

fig1 = figure;
ah = axes('Fontsize', 15);
for i=1:3
    Y(:,i) = binopdf(X,N,P(i));
    plot(X, Y(:,i), linestyle2{i,1}, 'linewidth', 3);
%     scatter(X, Y(:,i), linestyle2{i,1}, 'linewidth', 3);
    hold on;
end

xlim([0, 110]);
ylim([0, 0.15]);
title('The PMF of a binomial distribution');
xlabel('X');
ylabel('p_X');
legend(ah,'p=0.1','p=0.5', 'p=0.9','Location','NorthEast');
legend(ah,'boxoff')
saveas(fig1, 'D2E1.fig');
saveas(fig1, 'D2E1.eps', 'epsc');


%% Example 2
% Plot the CDF of a binomial distribution by varying the value for p

N = 100;
X = 1:100;
P = [0.1, 0.5, 0.9];
Y = zeros(100,3);
linestyle = cellstr(['-r'; '-b'; '-k'; '-g';'-m']);

fig2 = figure;
ah = axes('Fontsize', 15);
for i=1:3
    Y(:,i) = binocdf(X,N,P(1,i));
    stairs(X, Y(:,i), linestyle{i,1}, 'linewidth', 3);
    hold on;
end

xlim([0, 110]);
ylim([0, 1.0]);
title('The CDF of a binomial distribution');
xlabel('X');
ylabel('F_x');
legend(ah,'p=0.1','p=0.5', 'p=0.9','Location','SouthEast');
legend(ah,'boxoff')
saveas(fig2, 'D2E2.fig');
saveas(fig2, 'D2E2.eps', 'epsc');


%% Example 3
% Plot the PMF of a geometric distribution by varying p
%
% N = 100;
% p = {0.3, 0.5, 0.7}

N = 100;
X = 1:100;
P = [0.3, 0.5, 0.7];
Y = zeros(100,3);
linestyle = cellstr(['-.r'; '-.b'; '-.k'; '-.g';'-.m']);

fig3 = figure;
ah = axes('Fontsize', 15);
for i=1:3
    Y(:,i) = geopdf(X,P(1,i));
    %plot(X, Y(:,i), linestyle2{i,1}, 'linewidth', 3);
    scatter(X, Y(:,i), linestyle2{i,1}, 'linewidth', 3);
    hold on;
end

xlim([0, 110]);
ylim([0, 0.25]);
title('The PMF of a geometric distribution');
xlabel('X');
ylabel('p_X');
legend(ah,'p=0.1','p=0.5', 'p=0.9','Location','NorthEast');
legend(ah,'boxoff')
saveas(fig3, 'D2E3.fig');
saveas(fig3, 'D2E3.eps', 'epsc');

%% Example 4
% Plot the CDF of a geometric distribution by varying the value for p

N = 100;
X = 1:100;
P = [0.3, 0.5, 0.7];
Y = zeros(100,3);
linestyle = cellstr(['-r'; '-b'; '-k'; '-g';'-m']);

fig4 = figure;
ah = axes('Fontsize', 15);
for i=1:3
    Y(:,i) = geocdf(X,P(1,i));
    stairs(X, Y(:,i), linestyle{i,1}, 'linewidth', 3);
    hold on;
end

xlim([0, 110]);
ylim([0.5, 1.03]);
title('The CDF of a geometric distribution');
xlabel('X');
ylabel('F_x');
legend(ah,'p=0.1','p=0.5', 'p=0.9','Location','SouthEast');
legend(ah,'boxoff')
saveas(fig4, 'D2E4.fig');
saveas(fig4, 'D2E4.eps', 'epsc');